ATTP has been beating a bit on the carbon cycle, something Eli has talked about before. (Go ahead, Google is your friend bunnies) Some of that discussion, well it was ok, but a simple, grandmother level explanation came to Eli's mind.
There are lots of illustrations of the carbon cycle, most of them, like this one from GLOBE, with too much detail.
The second is the time needed to move carbon, mostly as animal shells falling to the bottom from the upper ocean into the deeps. The deep ocean reservoir is much bigger than the each of the surface reservoirs, more than thirty times as much, but the time needed to move carbon from the surface ocean to the bottom of the sea is a few hundred years.
The third is the incorporation of carbon dioxide into rocks, which is really slow, like over tens of thousands or years or more.
Because things happen at different rates, one can discuss each part of the cycle separately. Let the MOOC de Rabett start by looking at the fast processes. A really important insight is that two of the reservoirs, the surface biosphere and the ocean, are NOT connected to each other, but are linked through the atmosphere. A zeroth level model of this looks like
Keep this one on your phone to explain things to your favorite uncle over the upcoming holidays.
Anybunny wanting a more "mathematical" description of this could write out a series of rate equations and solve them (Excel with Euler integration works). In this system, Cx(t) is the amount of carbon in each of the reservoirs at time t, and kxy is the rate of exchange from reservoir x to y. E(t) describes the rate that carbon (dioxide) is injected into the atmosphere at time t. Note that the total amount of carbon in the three fast reservoirs is a constant